Use Newton's method to approximate a root of the equation In(4x) = arctan(x - 0.2) as follows. Let #₁ = 0.1 be the initial approximation. The fourth approximation 4 is and the fifth approximation is

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Use Newton's method to approximate a root of the equation \( \ln(4x) = \arctan(x - 0.2) \) as follows. Let \( x_1 = 0.1 \) be the initial approximation.

The fourth approximation \( x_4 \) is 

\[ \underline{\hspace{5cm}} \]

and the fifth approximation \( x_5 \) is 

\[ \underline{\hspace{5cm}} \]
Transcribed Image Text:Use Newton's method to approximate a root of the equation \( \ln(4x) = \arctan(x - 0.2) \) as follows. Let \( x_1 = 0.1 \) be the initial approximation. The fourth approximation \( x_4 \) is \[ \underline{\hspace{5cm}} \] and the fifth approximation \( x_5 \) is \[ \underline{\hspace{5cm}} \]
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